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16 Sep 2014, 01:19
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If a car had traveled 20 kilometers per hour faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 kilometers, at what speed did it travel ?
A. 35 kilometers per hour
B. 40 kilometers per hour
C. 50 kilometers per hour
D. 60 kilometers per hour
E. 65 kilometers per hour
A. 35 kilometers per hour
B. 40 kilometers per hour
C. 50 kilometers per hour
D. 60 kilometers per hour
E. 65 kilometers per hour
16 Sep 2014, 01:19
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Official Solution:
If a car had traveled 20 kilometers per hour faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 kilometers, at what speed did it travel ?
A. 35 kilometers per hour
B. 40 kilometers per hour
C. 50 kilometers per hour
D. 60 kilometers per hour
E. 65 kilometers per hour
Let the car's actual speed be \(x\) kilometers per hour. Then:
At a speed of \(x\) kilometers per hour, the car would cover 60 kilometers in \(time=\frac{distance}{rate}=\frac{60}{x}\) hours.
At a speed of \(x+20\) kilometers per hour, the car would cover 60 kilometers in \(time'=\frac{distance}{rate'}=\frac{60}{x+20}\) hours.
We're given that at the faster speed, the car takes 0.5 hours (or 30 minutes) less to cover the 60 kilometers. Therefore, \(\frac{60}{x} = \frac{60}{x + 20} + 0.5\).
At this stage, plugging in the answer options to back-solve is easier.
By doing so, we find that option B fits: \(\frac{60}{40} = 1.5\) and \(\frac{60}{40 + 20} + 0.5 = 1.5\).
Answer: B
If a car had traveled 20 kilometers per hour faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 kilometers, at what speed did it travel ?
A. 35 kilometers per hour
B. 40 kilometers per hour
C. 50 kilometers per hour
D. 60 kilometers per hour
E. 65 kilometers per hour
Let the car's actual speed be \(x\) kilometers per hour. Then:
At a speed of \(x\) kilometers per hour, the car would cover 60 kilometers in \(time=\frac{distance}{rate}=\frac{60}{x}\) hours.
At a speed of \(x+20\) kilometers per hour, the car would cover 60 kilometers in \(time'=\frac{distance}{rate'}=\frac{60}{x+20}\) hours.
We're given that at the faster speed, the car takes 0.5 hours (or 30 minutes) less to cover the 60 kilometers. Therefore, \(\frac{60}{x} = \frac{60}{x + 20} + 0.5\).
At this stage, plugging in the answer options to back-solve is easier.
By doing so, we find that option B fits: \(\frac{60}{40} = 1.5\) and \(\frac{60}{40 + 20} + 0.5 = 1.5\).
Answer: B
15 Oct 2023, 14:31
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
